Stochastic pH oscillations in a model of the urea-urease reaction confined to lipid vesicles

TL;DR

This study investigates stochastic pH oscillations within lipid vesicles containing the urea-urease reaction, revealing that intrinsic noise causes variability in oscillation periods while maintaining robustness in mean period for vesicles down to 200 nm.

Contribution

It introduces a stochastic model for pH oscillations in confined vesicles, highlighting the effects of molecular discreteness and noise on oscillation dynamics.

Findings

Intrinsic noise causes significant variation in oscillation periods.

Mean oscillation period remains stable for vesicles larger than 200 nm.

Oscillations are explained as a canard-like limit cycle, distinct from typical feedback oscillators.

Abstract

The urea-urease clock reaction is a pH switch from acid to basic that can turn into a pH oscillator if it occurs inside a suitable open reactor. We study the confinement of the reaction to lipid vesicles, which permit the exchange with an external reservoir by differential transport, enabling the recovery of the pH level and yielding a constant supply of urea molecules.For microscopically small vesicles, the discreteness of the number of molecules requires a stochastic treatment of the reaction dynamics. Our analysis shows that intrinsic noise induces a significant statistical variation of the oscillation period, which increases as the vesicles become smaller. The mean period, however, is found to be remarkably robust for vesicle sizes down to approximately 200 nm. The observed oscillations are explained as a canard-like limit cycle that differs from the wide class of conventional feedback oscillators.